LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Results (1-50 of 114 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1368.1.i.a	$1368$	$1$	1368.i	152.g	$2$	$1$	$1$	$0.683$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓				152.1.g.a	$2$	$0$	$-1$	$0$	$0$	$-1$		$1$		$q-q^{2}+q^{4}-q^{7}-q^{8}-q^{13}+q^{14}+\cdots$
1368.1.i.b	$1368$	$1$	1368.i	152.g	$2$	$1$	$1$	$0.683$	$\Q$	$D_{3}$	$\Q(\sqrt{-38}) $	None	✓				152.1.g.a	$2$	$0$	$1$	$0$	$0$	$-1$		$1$		$q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots$
1368.1.l.a	$1368$	$1$	1368.l	456.l	$2$	$4$	$4$	$0.683$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{38}) $		✓	✓	✓	1368.1.l.a	$8$	$0$	$0$	$0$	$0$	$0$		$2$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}^{2}q^{8}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
1368.1.ba.a	$1368$	$1$	1368.ba	1368.aa	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.ba.a	$4$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+q^{6}+\cdots$
1368.1.ba.b	$1368$	$1$	1368.ba	1368.aa	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.ba.b	$4$	$0$	$-1$	$2$	$0$	$0$		$1$		$q-\zeta_{6}q^{2}+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{6}+q^{8}+\cdots$
1368.1.ba.c	$1368$	$1$	1368.ba	1368.aa	$6$	$4$	$2$	$0.683$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓		1368.1.ba.c	$4$	$0$	$0$	$2$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots$
1368.1.bo.a	$1368$	$1$	1368.bo	1368.ao	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.bo.a	$4$	$0$	$-1$	$1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
1368.1.bo.b	$1368$	$1$	1368.bo	1368.ao	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.bo.a	$4$	$0$	$1$	$-1$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
1368.1.bt.a	$1368$	$1$	1368.bt	1368.at	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.bt.a	$4$	$0$	$-2$	$-1$	$0$	$0$		$1$		$q-q^{2}-\zeta_{6}q^{3}+q^{4}+\zeta_{6}q^{6}-q^{8}+\cdots$
1368.1.bt.b	$1368$	$1$	1368.bt	1368.at	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.bt.b	$4$	$0$	$2$	$1$	$0$	$0$		$1$		$q+q^{2}-\zeta_{6}^{2}q^{3}+q^{4}-\zeta_{6}^{2}q^{6}+q^{8}+\cdots$
1368.1.bw.a	$1368$	$1$	1368.bw	456.x	$6$	$8$	$4$	$0.683$	$\Q(\zeta_{24})$	$S_{4}$	None	None		✓	✓	✓	1368.1.bw.a	$8$	$0$	$0$	$0$	$0$	$-8$		$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-q^{7}+\zeta_{24}^{3}q^{8}+\cdots$
1368.1.bz.a	$1368$	$1$	1368.bz	152.k	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None			✓	✓	152.1.k.a	$4$	$0$	$1$	$0$	$0$	$0$		$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+q^{11}-\zeta_{6}q^{16}+\cdots$
1368.1.ce.a	$1368$	$1$	1368.ce	1368.be	$6$	$6$	$3$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		✓			1368.1.ce.a	$4$	$0$	$-3$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{6}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1368.1.ce.b	$1368$	$1$	1368.ce	1368.be	$6$	$6$	$3$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-38}) $	None		✓			1368.1.ce.a	$4$	$0$	$3$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{6}q^{2}+\zeta_{18}^{7}q^{3}-\zeta_{18}^{3}q^{4}+\cdots$
1368.1.cj.a	$1368$	$1$	1368.cj	1368.bj	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.ba.b	$4$	$0$	$2$	$-1$	$0$	$0$		$1$		$q+q^{2}+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{6}+q^{8}+\cdots$
1368.1.cj.b	$1368$	$1$	1368.cj	1368.bj	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.ba.a	$4$	$0$	$2$	$-1$	$0$	$0$		$1$		$q+q^{2}-\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{6}+q^{8}+\cdots$
1368.1.cj.c	$1368$	$1$	1368.cj	1368.bj	$6$	$4$	$2$	$0.683$	$\Q(\zeta_{12})$	$A_{4}$	None	None		✓	✓		1368.1.ba.c	$4$	$0$	$0$	$-4$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{3}-q^{4}-\zeta_{12}^{5}q^{5}+\cdots$
1368.1.cz.a	$1368$	$1$	1368.cz	1368.bz	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.bt.a	$4$	$0$	$-1$	$1$	$0$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{8}+\cdots$
1368.1.cz.b	$1368$	$1$	1368.cz	1368.bz	$6$	$2$	$1$	$0.683$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.bt.b	$4$	$0$	$1$	$2$	$0$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}+q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
1368.1.dh.a	$1368$	$1$	1368.dh	1368.ch	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.dh.a	$4$	$0$	$0$	$-3$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{6}q^{3}+\zeta_{18}^{8}q^{4}+\cdots$
1368.1.dh.b	$1368$	$1$	1368.dh	1368.ch	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.dh.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{8}q^{4}+\cdots$
1368.1.dk.a	$1368$	$1$	1368.dk	1368.ck	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.dk.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}q^{2}+\zeta_{18}^{2}q^{3}+\zeta_{18}^{2}q^{4}+\zeta_{18}^{3}q^{6}+\cdots$
1368.1.dk.b	$1368$	$1$	1368.dk	1368.ck	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.dk.b	$4$	$0$	$0$	$3$	$0$	$0$		$1$		$q-\zeta_{18}q^{2}-\zeta_{18}^{6}q^{3}+\zeta_{18}^{2}q^{4}+\zeta_{18}^{7}q^{6}+\cdots$
1368.1.ee.a	$1368$	$1$	1368.ee	1368.de	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.dk.a	$4$	$0$	$0$	$-6$	$0$	$0$		$1$		$q+\zeta_{18}^{4}q^{2}-q^{3}+\zeta_{18}^{8}q^{4}-\zeta_{18}^{4}q^{6}+\cdots$
1368.1.ee.b	$1368$	$1$	1368.ee	1368.de	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.dk.b	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{4}q^{2}-\zeta_{18}^{5}q^{3}+\zeta_{18}^{8}q^{4}+\cdots$
1368.1.eh.a	$1368$	$1$	1368.eh	152.u	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None			✓	✓	152.1.u.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+\zeta_{18}^{5}q^{2}-\zeta_{18}q^{4}-\zeta_{18}^{6}q^{8}+(-\zeta_{18}^{4}+\cdots)q^{11}+\cdots$
1368.1.en.a	$1368$	$1$	1368.en	1368.dn	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.dh.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{2}+\zeta_{18}^{4}q^{3}-\zeta_{18}q^{4}+q^{6}+\cdots$
1368.1.en.b	$1368$	$1$	1368.en	1368.dn	$18$	$6$	$1$	$0.683$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		✓			1368.1.dh.b	$4$	$0$	$0$	$6$	$0$	$0$		$1$		$q-\zeta_{18}^{5}q^{2}+q^{3}-\zeta_{18}q^{4}-\zeta_{18}^{5}q^{6}+\cdots$
1368.2.a.a	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓	✓			1368.2.a.a	$1$	$1$	$0$	$0$	$-4$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+6q^{11}+2q^{13}-4q^{17}-q^{19}+\cdots$
1368.2.a.b	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓				456.2.a.b	$1$	$0$	$0$	$0$	$-4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-4q^{5}+4q^{7}+4q^{11}-4q^{13}-6q^{17}+\cdots$
1368.2.a.c	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓				456.2.a.d	$1$	$1$	$0$	$0$	$-2$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{5}+2q^{13}-2q^{17}-q^{19}-q^{25}+\cdots$
1368.2.a.d	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓				456.2.a.a	$1$	$1$	$0$	$0$	$-1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-3q^{7}+5q^{11}-2q^{13}+q^{17}+\cdots$
1368.2.a.e	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1368.2.a.e	$1$	$1$	$0$	$0$	$0$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{11}-2q^{13}-4q^{17}+q^{19}-2q^{23}+\cdots$
1368.2.a.f	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1368.2.a.e	$1$	$0$	$0$	$0$	$0$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{11}-2q^{13}+4q^{17}+q^{19}+2q^{23}+\cdots$
1368.2.a.g	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓				152.2.a.b	$1$	$0$	$0$	$0$	$0$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{7}-2q^{11}+q^{13}+5q^{17}+q^{19}+\cdots$
1368.2.a.h	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓				152.2.a.a	$1$	$1$	$0$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-3q^{7}+3q^{11}-4q^{13}-5q^{17}+\cdots$
1368.2.a.i	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓				456.2.a.c	$1$	$0$	$0$	$0$	$3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{5}-3q^{7}+q^{11}-2q^{13}+5q^{17}+\cdots$
1368.2.a.j	$1368$	$2$	1368.a	1.a	$1$	$1$	$1$	$10.924$	$\Q$	$_{}$	None	None	✓	✓			1368.2.a.a	$1$	$0$	$0$	$0$	$4$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{5}-6q^{11}+2q^{13}+4q^{17}-q^{19}+\cdots$
1368.2.a.k	$1368$	$2$	1368.a	1.a	$1$	$2$	$2$	$10.924$	$\Q(\sqrt{17}) $	$_{}$	None	None	✓		✓		456.2.a.f	$1$	$1$	$0$	$0$	$-1$	$1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{5}+\beta q^{7}+(-4+\beta )q^{11}-2\beta q^{13}+\cdots$
1368.2.a.l	$1368$	$2$	1368.a	1.a	$1$	$2$	$2$	$10.924$	$\Q(\sqrt{41}) $	$_{}$	None	None	✓		✓		456.2.a.e	$1$	$0$	$0$	$0$	$1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{5}+(-2+\beta )q^{7}+(-2+\beta )q^{11}+\cdots$
1368.2.a.m	$1368$	$2$	1368.a	1.a	$1$	$3$	$3$	$10.924$	3.3.892.1	$_{}$	None	None	✓	✓	✓		1368.2.a.m	$1$	$0$	$0$	$0$	$-2$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots$
1368.2.a.n	$1368$	$2$	1368.a	1.a	$1$	$3$	$3$	$10.924$	3.3.961.1	$_{}$	None	None	✓		✓	✓	152.2.a.c	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{5}+(1-\beta _{2})q^{7}+(2-\beta _{1})q^{11}+\cdots$
1368.2.a.o	$1368$	$2$	1368.a	1.a	$1$	$3$	$3$	$10.924$	3.3.892.1	$_{}$	None	None	✓	✓	✓		1368.2.a.m	$1$	$1$	$0$	$0$	$2$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{5}+(-1+\beta _{1}+\beta _{2})q^{7}+\cdots$
1368.2.e.a	$1368$	$2$	1368.e	152.b	$2$	$2$	$2$	$10.924$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None					152.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta q^{2}-2q^{4}+2\beta q^{8}-6q^{11}+4q^{16}+\cdots$
1368.2.e.b	$1368$	$2$	1368.e	152.b	$2$	$4$	$4$	$10.924$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None					152.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(1-\beta _{3})q^{4}+(-1+2\beta _{3})q^{7}+\cdots$
1368.2.e.c	$1368$	$2$	1368.e	152.b	$2$	$8$	$8$	$10.924$	8.0.$\cdots$.11	$_{}$	$\Q(\sqrt{-114}) $	None		✓			1368.2.e.c	$8$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{8}+\cdots$
1368.2.e.d	$1368$	$2$	1368.e	152.b	$2$	$8$	$8$	$10.924$	8.0.207360000.1	$_{}$	None	None		✓			1368.2.e.d	$8$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{4})q^{4}+2\beta _{4}q^{7}+\cdots$
1368.2.e.e	$1368$	$2$	1368.e	152.b	$2$	$12$	$12$	$10.924$	12.0.$\cdots$.1	$_{}$	None	None					152.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{5}-\beta _{8})q^{5}-\beta _{8}q^{7}+\cdots$
1368.2.e.f	$1368$	$2$	1368.e	152.b	$2$	$24$	$24$	$10.924$		$_{}$	None	None		✓			1368.2.e.f	$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1368.2.e.g	$1368$	$2$	1368.e	152.b	$2$	$40$	$40$	$10.924$		$_{}$	None	None			✓		456.2.e.a	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.